With the help of standard deviation we can conclude our answer.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical texts and equations to indicate standard deviation. Standard deviation may be written as SD.acc to our question-
total sample of wool fibres = 20thus the sample mean = 436.05hence the sd= 11.9learn more about standard deviation here:
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a passenger train traveled 240 miles in the same amount of time it took a freight train to travel miles. the rate of the freight train was miles per hour slower than the rate of the passenger train. find the rate of the passenger train.
The rate of the passenger train is 60mph.
We know that,
Speed = Distance / Time
Time = Distance / Speed
s = speed of passenger train
speed of freight train = (s - 20)
T = 240 / s
T = 160 / (s-20)
240 / s = 160 / (s-20)
240(s - 20)/s(s - 20) = 160s/s(s - 20)
240(s - 20)/s(s - 20) - 160s/s(s - 20) = 0
240(s - 20) - 160s = 0s(s - 20)
240s - 4800 - 160s = 0
80s - 4800 = 0
80s = 4800
Hence the speed of the freight train is 40mph, while the speed of the passenger train is 60mph.
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an important issue facing americans is the large number of medical malpractice lawsuits and the expenses that they generate. in a study of 1228 randomly selected medical malpractice lawsuits, it is found that 856 of them were later dropped or dismissed (based on data from the physician insurers association of america). construct a 99% confidence interval estimate of the proportion of medical malpractice lawsuits that are dropped or dismissed.
About [0.7479, 0.8091] of medical malpractice cases are abandoned or dismissed, according to the estimate with a 95% confidence level.
A confidence interval is a method for estimating a population parameter, such as the population proportion, at a given level of confidence, using the sample statistic, such as the sample proportion, and the confidence coefficient, such as the critical value.
arbitrary sample size, n = 1228
number of those who were dropped or dismissed, x = 856
The sample percentage of later discarded or dropped, p = 956 / 1228 ≅ 0.7785
Level of confidence = 0.99
Level of significance α = 0.01
The population proportion's 99% confidence interval estimate is calculated as follows:
p ± [tex]z_{a/2}[/tex] * [tex]\sqrt\frac{p (1 - p)}{n}[/tex]
Using the Excel function or the z-distribution table for calculation
[tex]z_{a/2} = z_{0.01/2} = z_{0.005}[/tex]
=NORMSINV(0.05)
[tex]z_{0.01/2}[/tex] ≅ ±2.58
The interval's computation is as follows:
0.7785 ± 2.58 * [tex]\sqrt\frac{0.7785 (1 - 0.7785)}{1228}[/tex]
= 0.7785 ± 2.58 * 0.0118
= = 0.7785 ± 0.0306
(0.7479, 0.8091)
As a result, the estimate of the proportion of medical malpractice claims that are withdrawn or dismissed at a 99 percent confidence interval is roughly [0.7479, 0.8091].
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PLEASE PLEASE HELP ME WITH THIS QUESTION Two systems of equations are given below.
For each system, choose the best description of its solution.
If applicable, give the solution.
PLEASE HELP!! WILL GIVE BRAINLIEST
The mass of a test sample is 10g, and it has the volume of 2.5cm^3 . What is its density?
A. 10g/cm^3
B. 2.5cm^3/g
C. 4g/cm^3
D. 4cm^3/g
E. 0.25g/cm^3
Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.
Define density.The ratio of an object's mass to its volume is its density. Grams per cubic centimeter, or g/cm³, are frequently used to measure density. Keep in mind that a volume is measured in cubic centimeters, not gram (the same volume as 1 milliliter). More particles will make a box denser than fewer particles in the same box. Despite the fact that the SI unit of density is kg/m³, we instead use g/cm³ for solids, g/ml for liquids, and g/L for gases out of convenience. The relationship between a substance's mass and the volume it occupies is known as its density.
Given,
Volume = 2.5 cm³
Mass = 10 g
For density:
Mass ÷ volume
10 ÷ 2.5
4
Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.
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there are 5 major sea islands in the queen elizabeth islands of canada that you are interested in visiting. there are 12 major lakes in saskatchewan, canada that you would also like to visit. (a) if you are planning a trip to visit one of these islands, followed by one of these lakes, how many different trips could you make?
The person can make 60 trips.
Let us say that A indicates the major sea Islands and B indicates the major lakes. Taking both the cases as events, we will use multiplication principle. Based on the information, the event A occurs in m ways and the event B will occur in n ways. So, the two events will occur in m×n ways.
Thus, A × B = 5 × 12
Performing multiplication on Right Hand Side of the equation to find the number of trips
Total number of trips = 60
Hence, there are 60 trips that could be made.
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for g(x)=x to the power of 2 minus x, find g(x) when x=-2
The value of the function g(x) when x = -2 is 6
How to evaluate the function?The definition of the function is given as
g(x)=x to the power of 2 minus x
Rewrite the above function properly
So, we have the following representation
g(x) = x² - x
To find the function g(-2), we set the value of x in the equation g(x) = x² - x to -2
This is represented by
Calculate g(x), when x = -2
Substitute -2 for x in the equation g(x) = x² - x
So, we have the following equation
g(-2) = (-2)² - (-2)
Evaluate the exponents
This gives
g(-2) = 4 - (-2)
Evaluate the sum
g(-2) = 6
Hence, the value of the function is 6
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3) Justin made some cookies for the holiday. She baked 10 sugar cookies, 18 chocolate chip cookies, and 15 ginger cookies. What is the ratio of sugar cookies to ginger cookies in simplest form?
a new shopping mall is gaining in popularity. every day since it opened, the number of shoppers is 5% more than the number of shoppers the day before. about how many total shoppers would be expected after 10 days, if there were 100 shoppers on the first day?
After 10 days, the expected number of shoppers at the shopping mall is 163.
It is given that the number of shoppers increases daily by 5% from the number of shoppers the previous day.
As we can see that the increase in the number of shoppers is going to change every day, and the above case is compounded daily.
The formula of compound increase is
Amount = Base X (1 + r/n)ⁿˣ
where,
Base = original amount
r = rate of change
n = no. of times the change occurs in the time period
t = time
Here,
Base = 100
r = 5/100
n = 1, since it changes once every day
x = 10
Therefore we get
100 X (1 + 5/100)¹⁰
= 100 X 1.05¹⁰
162.88
Since the number of people cannot be in decimal,
the expected number of people is 163
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There are 10 girls and 20 boys in a class.
The class has a test.
The mean mark for all the class is 70
The mean mark for all the boys is 62
Work out the mean mark for the girls.
Answer:
86
Step-by-step explanation:
mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
given mean mark for class of 30 is 70 , then
[tex]\frac{sum}{30}[/tex] = 70 ( multiply both sides by 30 )
sum = 2100
given the mean mark for 20 boys is 62, then
[tex]\frac{sum}{20}[/tex] = 62 ( multiply both sides by 20 )
sum = 1240
the sum for the 10 girls is then 2100 - 1240 = 860
then mean score for the 10 girls is
mean = [tex]\frac{860}{10}[/tex] = 86
{2x+7y=-20
{x-3y=16
Solve for systems of equations
By solving the linear equations we get the final values of x = 4 & y = 4.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order term are included.
We have,
2x + 7y = -20 ----------(i)
x - 3y = 16 ----------(ii)
By multiplying equation (ii) with 2 we get,
2x + 7y = -20 ---------(III)
2x - 6y = 32 -----------(IV)
taking subtraction of equations (III) and (IV), we get
y = 4
by putting value of y in equation (ii) we get,
x = 4
Hence by solving the linear equations we get the values of x = 4 & y = 4.
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in a class of 150 students the ratio of boys to girls is 3 2 how many more boys than girls are in the class
The number of boys and girls in a class of 150 students is 90 and 60 respectively.
RATIO:
Comparing two quantities of the same units and determining the ratio tells us how much of one quantity is in the other.
i.e., it shows how many times a number contains another.
Total number of students = 150
ratio of boys to girls = 3 : 2
B:G = 3 : 2
now
3x + 2x = 150
5x = 150
x = 30
the number of boys = 3x = 3 X 30 = 90 boys.
the number of girls = 2x = 2 X 30 = 60 girls.
The number of boys and girls in a class of 150 students is 90 and 60 respectively.
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Absolutely value equations |m-2|-1=4
The value of 'm' in the absolute value equation is 3
What is a linear equation?A linear equation can be described as an equation having the highest power of the variable as 1.
It is also referred to as a one-degree equation.
Example;
x + 1 = 4
What is absolute value?Absolute value of a number can be defined as the value of that number irrespective of its direction to zero on the number line.
The value must take a positive sign.
The symbol used to represent the absolute value of a number is '| '
We have the equation;
|m-2|-1=4
Let's take the absolute value
m + 2 - 1 = 4
Now, collect like terms, we get;
m = 4 - 1
Add or subtract like terms
m = 3
Hence, the value is 3
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a gardener has 1040 feet of fencing to fence in a rectangular garden. one side of the garden is bordered by a river and so it does not need any fencing. garden bordered by a river what dimensions would guarantee that the garden has the greatest possible area?
The dimensions 520 by 360 feet would guarantee that the garden has the greatest possible area .
Let length be l and width be b of garden .
According to question ,
l + 2b = 1040
Area of garden = l * b
Substituting value of l in formula for area ,
Area = ( 1040 - 2b ) * b = 1040b - 2[tex]b^{2}[/tex]
Taking derivative of Area wrt. b and putting it equal to 0 ,
1040 - 4b = 0
b = 1040 / 4
b = 260 feet
Therefore , l = 1040 - 520 = 520 feet .
Maximum Area = 260 * 520 = 135200 [tex]feet^{2}[/tex] .
Hence , the dimensions 520 by 360 feet would guarantee that the garden has the greatest possible area .
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Triangle FGH has vertices F(-3, 4), G(2, 0), and H(-1, -2). Graph AFGH and its image after a rotation of 180° about (-3, -6).
Answer:
Im gonna assume its counter clockwise (excuse the bad drawing)
Step-by-step explanation:
The vertices of triangle F'G'H' after a rotation of 180° about (-3, -6) are F'(0, 10), G'(5, 6) and H'(2, 4).
What is rotation?Rotations are transformations that turn a shape around a fixed point. To rotate a shape we need: a centre of rotation. an angle of rotation (given in degrees) a direction of rotation – either clockwise or anti-clockwise.
Given that, triangle FGH has vertices F(-3, 4), G(2, 0), and H(-1, -2).
180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).
So, (x, y) → (x+3, y+6)
F(-3, 4) → (-3+3, 4+6) → F'(0, 10)
G(2, 0) → (2+3, 0+6) → G'(5, 6)
H(-1, -2) → (-1+3, -2+6) → H'(2, 4)
Therefore, the vertices of triangle F'G'H' after a rotation of 180° about (-3, -6) are F'(0, 10), G'(5, 6) and H'(2, 4).
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By increasing the pendulum's mass and releasing the pendulum from a greater height the maximum potential energy
will increase and the maximum kinetic energy will decrease.
Answer: False
Step-by-step explanation:The potential energy will decrease and the kinetic will increase
You deposit $3000 in an account that
earns simple interet at an annual rate of
5%. How long must you leave the money
in the account to earn $500 in interest?
Answer:
3 ¹/₃ years
Step-by-step explanation:
Simple Interest Formula
I = Prt
where:
I = Total interest.P = Principal amount.r = Annual interest rate (in decimal form).t = Time (in years).Given:
I = $500P = $3,000r = 5% = 0.05Substitute the given values into the formula and solve for t:
[tex]\sf \implies 500=3000 \times 0.05 \times t[/tex]
[tex]\sf \implies 500=150t[/tex]
[tex]\sf \implies t=\dfrac{500}{150}[/tex]
[tex]\implies \sf t=3\frac{1}{3}[/tex]
Therefore, the money must be left in the account for 3 ¹/₃ years for the account to earn $500 interest.
A gigameter is 1.0×10^6 kilometers. How many square kilometers are in 5 square gigameters?
Write your answer in scientific notation.
The number of kilometers in 5 square gigameters is 5. 0 × 10^18
What is proportion?Proportion can be described as an expression or equation in which two ratios are made equal to each other.
It is also known as the mathematical comparison between two numbers or elements.
From the information given, we have;
1 gigameter = 1.0×10^6 kilometers
But,
5 square gigameters = 5. 1.0×10^6 . 1.0×10^6
Add the powers
5 square gigameters = 5..0×10^12
If 1 gigameter = 1.0×10^6 kilometers
Then 5. 1.0×10^12 gigameter = x
cross multiply
x = 5.0×10^12 × 1.0×10^6
x = 5. 0 × 10^18 kilometers
Hence, the value is 5. 0 × 10^18 kilometers
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The weight of four different boxes is shown in pounds. Which list shows the weights in order from least to greatest?
16.4, 16 1/2, 16.625 , 16 3/5
Answer: 16.4, 16 1/2, 16 3/5 16.625,
Step-by-step explanation: 16.4, 16 1/2, 16 3/5 16.625,
16 1/2 = 16.5, 16 3/5 = 16.6
1. Name a plane parallel to plane WXT
2. Name two segments parallel to VU.
3. Name two segments parallel to SW.
4. Name two segments skew to XY.
5. Name two segments skew to VZ.
The plane which is parallel to the line WXT is UVZW
two segments parallel to VU is ST and WX
two segments skew to XY is UT
two segments skew to VZ is YU and TX
What are parallel lines ?Lines that are always the same distance apart in a plane are said to be parallel. Lines that are parallel never cross. Lines that cross at a straight angle (90 degrees) are said to be perpendicular.
Given : The quadrilateral prism
Parallel lines means lines which does not interact and run parallel meaning they have equal distance between them.
The plane which is parallel to the line WXT is UVZW
two segments parallel to VU is ST and WX
two segments skew to XY is UT
two segments skew to VZ is YU and TX
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a homeowner wants to fence in a rectangular space in her yard along one side of her house for her dogs. the total area she can fence in is 650 square feet.
write an expression to find the area of the fenced region.
The required expression for the fenced region is lw = 650.
Given that,
A homeowner wants to fence in a rectangular space in her yard along one side of her house for her dogs. the total area she can fence in is 650 square feet.
What is a rectangle?
The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.
Here,
Let the length of the area be l and the width of the area be w,
The total area she can fence in is 650 square feet.
lw = 650
Thus, the required expression for the fenced region is lw = 650.
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Can anyone answer question 8?
The Question: An employer provides two payment options for employees.
Option A: Receive $200 the first week. Receive an additional $50 for each of the following weeks.
Option B: Receive $200 the first week. Receive an additional 10% for each of the following weeks.
My Answer: Option A; 200, 250, 300, 350, 400, 450. Option B; 200, 220, 242, 266.2, 292.82, 322.1
Am I correct?
Answer:
Your first option is correct but your second is wrong
Step-by-step explanation:
In option b-
when an employee receives 10% additional for each of the following weeks:
10% of 200= 10/100 x200= 20
it means he will get $20 in extra in every week
so it will be- 220,240,260
2.2(s + 1) 14.7 = 5.1
Answer:-454/539
Step-by-step explanation:32.34(s+1)=5.1
32.34s+32.34=5.1
32.34s=5.1-32.34
32.34s=-27.24
s=-454/539
what's the answer to
m + 6n; use m = 6, and n = 6
Answer:
Step-by-step explanation:
1. Put the variable as numbers in the computation. m=6 and n=6
SO:
6+6*6
2. Compute using Pemdas( Parentheses, exponets,multiplication, division, addition, subtraction)! Or order of operations!
6+36= 42
Answer: 42
Use remainder theorem for x^3+8x^2+11x-20 by (x+4)
Answer:
x^3 + 64 + 11x - 20bxy - 80by
(if I am wrong, apologies)
Answer:
x^2+4x-5
Step-by-step explanation:
x^3+8x^2+11x-20/x+4=x^2+4x-5
The ratio of money in Brian's wallet to
Colin's wallet one day was 7:2.
Brian spent £39 that day.
Brian now had £4 less than Colin.
How much did Brian initially have?
Brian has £63 Initially, by using the ratio and proportion method.
What are Ratio and Proportion?
In this section, the terms ratio and percentage are defined. Both ideas play a significant role in mathematics. Numerous examples where the notion of the ratio is highlighted may be found in daily life, such as the rate of speed (distance/time) or price (rupees/meter) of a substance.
An equation known as proportion shows that the two ratios presented are equal to one another. For instance, the time it takes a train to go 100 kilometers per hour is equal to the time it needs to travel 500 kilometers in five hours. Example: 100 km/hr = 500 km/5 hour. The division technique of comparing two amounts can be quite effective in some circumstances. We can argue that a ratio is a comparison or condensed form of two quantities of the same type. We may determine how many times one quantity is equal to another using this relationship. The ratio may be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects. A ratio is indicated by the symbol ":".
In the question, It is given that:
The ratio of money in Brian's wallet to Colin's wallet one day was 7:2.
Let 7x denotes the amount in Brian's wallet and 2x denote the amount in Colin's wallet on that day.
we know that:
Brian spent £39 that day.
Amount left in Brian's wallet = 7x- 39
Brian now had £4 less than Colin.
⇒ 2x -4= 7x- 39
⇒ 7x-2x=4+39
⇒ 5x=35
⇒ x=7 [Divide both sides by 5 ]
So , The initial amount in Brian's wallet = 7(7)= £49
The initial amount in Colin's wallet = 2(7)= £14
The amount they had together = £49+£14 = £63
So, They had £63 altogether initially.
Therefore, Brian has £63 Initially.
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Answer: £14
Step-by-step explanation: Because Hegarty Maths says it is when I got this same Question Wrong :(PAGE 6
7. Maymont Middle School is selling tickets for the winter musical. Adult tickets cost $5 each and child
tickets cost $3 each.
a. Write a mathematical equation that represents the total cost, t, for a adult tickets and c child tickets.
b. Ciera has $28. Could she buy 2 adult tickets and 7 child tickets? Use your equation from part a. to show
your work.
c. Jaylen has $22. If he buys 2 adult tickets, how many child tickets can he buy? Show your work.
C2022 Iluminate Education, Inc.
Question
Edit ->
Edit ->
Ĉ
Question 7b
Ĉ
Fo
Form
a) A mathematical equation that represents the total cost, t, for a adult tickets and c child tickets is t = $5a + $3c.
b)No, she cannot buy 2 adult tickets and 7 child tickets.
Define equation.Mathematical equations are relationships between two expressions that are equal on both sides of the equal to sign. An equation is, for instance, 3y = 16.
Given,
Maymont Middle School is selling tickets for the winter musical. Adult tickets cost $5 each and child tickets cost $3 each.
a) Mathematical equation:
represents the total cost, t, for a adult tickets and c child tickets
t = $5a + $3c
A mathematical equation that represents the total cost, t, for a adult tickets and c child tickets is t = $5a + $3c.
b) Ciera has $28.
a = 2 c = 7
Equating values in equation,
= $5(2) + $3(7)
= $10 + $27
= $37
No, she cannot buy 2 adult tickets and 7 child tickets.
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A 12 pack of sodas is priced at $5.40 and a 16 pack of sodas is priced at $6.72. Which is a better buy?
Answer:
Step-by-step explanation:
5.40/12= 0.45
6.72/16=0.42
Answer:
The 16 pack
Step-by-step explanation:
Pack 1: $5.40 for 12
Find the price per soda by dividing the price by 12: $5.40 / 12 = $0.45 per canPack 2: $6.72 for 16
Find the price per soda by dividing the price by 16: $6.72 / 16 = $0.42Therefore the 16 pack is the better buy because you purchase an extra 4 sodas for $0.03 less.
Sutton takes 48 minutes to walk to work. after getting a new job, sutton takes 30.72 minutes to walk to work. what was the percent decrease in the travel time?
The percent decrease in the travel time after getting a new job is 36%.
Percentage is defined as part of a whole expressed in hundredths or out of 100. It is usually written with the symbol "%".
First, determine the decrease in travel time after getting a new job by subtracting the new travel time of 30.72 minutes from the initial travel time of 48 minutes.
decrease in time = 48 - 30.72
decrease in time = 17.28
Then, determine the percent decrease by dividing the decrease in time of 17.28 minutes by the initial travel time of 48 minutes and multiply by 100.
percent decrease = (17.28 / 48) x 100
percent decrease = 36%
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Nora leans a 24-foot ladder against a wall so that it forms an angle of 76^{\circ} ∘ with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
23.29 ft
Step-by-step explanation:
The given scenario can be modelled as a right triangle, where the angle between the ground and the ladder is 76°, the side opposite the angle is the height the ladder reaches up the wall, and the hypotenuse is the ladder.
To find how high up the wall the ladder reaches, use the sine trigonometric ratio:
[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]
where:
θ is the angle.O is the side opposite the angle.H is the hypotenuse (the side opposite the right angle).The angle of elevation is 76°, so θ = 76°.
Let x be the height the ladder reaches up the wall, so O = x.
H is the length of the ladder, so H = 24.
Substitute the given values into the sine ratio and round the answer to the nearest hundredth:
[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]
[tex]\sin(76^{\circ})= \dfrac{x}{24}[/tex]
[tex]\sin(76^{\circ})\cdot 24= \dfrac{x}{24}\cdot 24[/tex]
[tex]24 \sin(76^{\circ})= x[/tex]
[tex]x=24 \sin(76^{\circ})[/tex]
[tex]x=23.28709743...[/tex]
[tex]x=23.29\; \sf ft\;(nearest\;hundredth)[/tex]
Therefore, the ladder reaches 23.29 ft up the wall, rounded to the nearest hundredth.
